Changing reference cells without changing data

I have a sheet that auto assigns a task to workers, in order, using a basic index and Vlookup. The list of workers is in a different sheet.

I have a worker getting pulled to work on a special project for a few months whose name I wish to remove from the list.

How do I pull her name from the list without changing the list of every task she did prior to her reassignment? (Without copy pasting every previous cell of the worksheet into itself without formatting.)

I've tried locking (the formula was still there, so it still changed all my old cells when I removed her from the list) and freezing (which didn't help at all), but neither did what I wanted.